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dc.contributor.authorDujardin, G. M.
dc.date.accessioned2016-02-25T12:43:18Z
dc.date.available2016-02-25T12:43:18Z
dc.date.issued2009-08-12
dc.identifier.citationDujardin GM (2009) Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465: 3341–3360. Available: http://dx.doi.org/10.1098/rspa.2009.0194.
dc.identifier.issn1364-5021
dc.identifier.issn1471-2946
dc.identifier.doi10.1098/rspa.2009.0194
dc.identifier.urihttp://hdl.handle.net/10754/597627
dc.description.abstractThis paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.
dc.description.sponsorshipThe author thanks A.S. Fokas and P.A. Markowich for their ideas and comments on this work. This publication is based on work supported by Award No. KUK-I1-007-43, made by the King Abdullah University of Science and Technology.
dc.publisherThe Royal Society
dc.subjectApplied mathematics
dc.subjectDifferential equations
dc.subjectInitial boundary value problems
dc.subjectLong-time behaviour
dc.subjectPeriodic data
dc.titleAsymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals
dc.typeArticle
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
kaust.grant.numberKUK-I1-007-43


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